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Stochastic Modeling for Climate Change Velocities Gelfand, Alan


The ranges of plants and animals are moving in response to change in climate. In particular, if temperatures rise, some species will have to move their range. On a fine spatial scale, this may mean moving up in elevation; on a larger spatial scale, this may result in a latitudinal change. In this regard, the notion of velocity of climate change has been introduced to reflect change in location corresponding to change in temperature. If location is viewed as one dimensional, say $x$ and time is denoted by $t$, the velocity becomes $dx/dt$. In the crudest form, given a relationship between temperature (Temp) and time as well as a relationship between Temp and location, we would have $\frac{dx}{dt} =\frac{dTemp}{dt} /\frac{Temp}{dx}$. The contribution here is to extend this simple definition to more realistic models, models incorporating more sophisticated explanations of temperature, models introducing spatial locations, and, most importantly, models that are stochastic over space and time. With such model components, we can learn about directional velocities, with uncertainty. We can capture spatial structure in velocities. We can assess whether velocities tend to be positive or negative, and in fact, whether and where they tend to be significantly different from 0. Extension of the model development can be envisioned to the species level, i.e., to species- specific velocities. Here, we replace a temperature model as the driver with presence-only or presence/absence models. We can make attractive connections to customary advection and diffusion specifications through partial differential equations. We illustrate with 118 years of data at 10 km resolution (resulting in more than 21,000 cells) for the eastern United States. We adopt a Bayesian framework and can obtain posterior distributions of directional velocities at arbitrary spatial locations and times. This is joint work with Erin Schliep.

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